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Statistics chapter 13
ANOVAs
32
Mathematics
Undergraduate 1
05/08/2007

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Term
 When do we use an independent measures ANOVA?
Definition
 when there is more than 2 groups or levels of the IV
Term
 What's the difference between independent measures, repeated measures, and mixed ANOVA designs?
Definition
 independent:repeated:mixed: more than 1 IV at the same time
Term
 What is generally learned from ANOVA?
Definition
 Tells whether means of samples that undergo different levels of the IV come from populations with the same or different means.
Term
 What are the hypotheses for ANOVAs?
Definition
 H0: μ1 = μ2 = μ3 = …μkH1: At least one μ is different from others.
Term
 Why do we need ANOVA when a series of t tests would test several hypotheses?
Definition
 The overall chance of type 1 error is the sum of all individual scores --> if you conduct 5 HT at alpha .05, the end chance of type 1 error is .25. It is also a lot more work.
Term
 What is the difference between test-wise and experiment-wise alpha level?
Definition
 test-wise: level of error set for 1 testexperiment-wise: level of all tests combined on 1 set of data or study*every test conducted increases 2nd type of alpha level
Term
 How does ANOVA help with the experiment-wise alpha level?
Definition
 makes all comparisons between means simultaneous and keeps alpha at level set by experimentor (even if compare many levels or groups)
Term
 Independent Variable
Definition
 is the variable manipulated– Called a factor in ANOVA designs– May have many factors in experiment
Term
 Quasi-Independent Variable
Definition
 not actively manipulated, but may affect experiment (ie gender, age, education, etc)
Term
 Factor
Definition
 Variable that designates the groups being compared
Term
 Between-Treatments Variance
Definition
 calculate the variance between treatment groups to provie a measure of the overall differences between treatment conditions --> really measures the differences between sample means
Term
 Within-Treatments Variance
Definition
 The variability within each sample --> provides a measure of the variability inside each treatment condition
Term
 Why is variance partitioned in ANOVA?
Definition
 In this way ANOVA shows if differences between sample means are greater thanwould be expected by chance.
Term
 Error term
Definition
 The MS value in the denominator of the F-ratio is called the error term. This MS value is intended to measure the amount of error variability - variability in the data for which there is no systematic or predictable explanation. It is used as a standard for determining whether or not the differences between treatments (measured by MSbtwn) are greater than would be expected just by chance.
Term
 Numerator of F-ratio
Definition
 MSbetween - simply measure how much difference exists between the treatement means. The bigger the mean differences, the bigger the F-ratio.
Term
 Denominator of F-ratio
Definition
 MSwithin - measures the variance of the scores inside each treatment; that is, the variance for each of the separate samples. In general, the larger the sample variances, the smaller is the F-ratio.
Term
 What contributes to the between groups source of variance in the independent measures ANOVA?
Definition
 MSbetween is composed of (SSbetween) / (dfbetween)
Term
 What contributes to teh within group source of variance in this test?
Definition
 MS within = (SSwithin) / (dfwithin)
Term
 k
Definition
 the number of individual treatment conditions; the number of levels of treatments
Term
 n
Definition
 the number of raw scores in each individual treatment condition
Term
 N
Definition
 total number of raw scores in the entire study; OR k times n, when n is constant
Term
 T
Definition
 sum of all scores in the entire study (sigma X)
Term
 G
Definition
 grand total, sum of all scores in the entire study (sigma T)
Term
 F
Definition
 MS between /MS within
Term
 F distribution
Definition
 - family of curves based on 2 separate dfs- tells all values F could be and probability of getting each- all F values are positive because they are variances- positively skewed (always 1-tailed)- median value is about 1; the more extreme the Fobt, the more likely you can reject Ho- Fobt = 1.00 --> retain null
Term
 Why do we need 2 dfs to look up a critical F value?
Definition
 df between (numerator) --> topdf within (denominator) --> down side
Term
 What assumptions are required for IM ANOVA?
Definition
 - scores are drawn from normal distributions (large enough sample size)- homogeneity of variance (errors are unrelated)- observations are independent- violations of assumptions dealt with in separate tests after F test is run* the only way groups can differ is in their means
Term
 How is sample variance accounted for in ANOVA?
Definition
 – MSwithin works like s^2p
Term
 When does F = t2?
Definition
 – When using 2 groups / treatmen conditions– ANOVA may be used with 2 groups, undercertain conditions
Term
 effect size (n^2)
Definition
 - Percentage of variance accounted fordue to treatment- Tells how much of variabilitybetween scores explained by treatment effectη = SSb / SSt
Term
 What is a post hoc test?
Definition
 Determine which μ or μs actuallydifferent from others– Pairwise comparisons compare just 2 μs–May be planned or unplanned–Must keep experiment-wise alpha inmind to avoid Type I error so don’t run too many…- designed to reduce type 1 error
Term
 Give 2 examples of post hoc tests
Definition
 1. Dunn test: divide alpha by number of planned comparisons – Plan 2 post hoc comparisons – 0.05/2 = 0.025 is new alpha for each post hoc test2. Tukey’s HSD: Single value determines minimum difference between treatments necessary for significance - better for unplanned comparisonsHSD = q (sq.rt. MSw/n)
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